Your Thermometer Can't Measure Below Freezing? Here's Another Approach!

Calculus Level 3

Andrew is very curious how cold it is outside, but he does not want to venture there for too long. Furthermore, his (home-made) thermometer is unable to measure below \( 0 ^\circ C \), and it's definitely way below freeing out there.

The thermometer currently shows a room temperature to \(21^{\circ} C\). Andrew takes the thermometer outside and one minute later it shows \(13^{\circ} C\). After another minute it shows \(6^{\circ} C\). Fed up with the cold, Andrew heads back indoor for warmth. What is the outside temperature, in \(^{\circ} C\)?

Note: Newton's Law of Cooling states that the rate of change of its temperature is proportional to the difference of its temperature and the temperature of its surroundings.

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